Perturbation theory for the nonlinear Schrödinger equation with a random potential

DOI10.1088/0951-7715/22/12/004zbMath1204.37074arXiv0901.4951OpenAlexW2057523923MaRDI QIDQ3652639

Yevgeny Krivolapov, Shmuel Fishman, Avy Soffer

Publication date: 15 December 2009

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.4951

zbMATH Keywords

latticeperturbationnonlinear Schrödinger equationrandom potentialprobabilistic bound

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Nonlinear first-order PDEs (35F20) NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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KAM TORI AND ABSENCE OF DIFFUSION OF A WAVE-PACKET IN THE 1D RANDOM DNLS MODEL ⋮ Long-time Anderson localization for the nonlinear Schrödinger equation revisited ⋮ Perturbation theory for nonlinear Schrödinger equations ⋮ A numerical and symbolical approximation of the nonlinear Anderson model ⋮ Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain ⋮ Statistical properties of the one dimensional Anderson model relevant for the nonlinear Schrödinger equation in a random potential ⋮ Asymptotic quantum many-body localization from thermal disorder ⋮ Multifractals competing with solitons on Fibonacci optical lattices ⋮ An eigensystem approach to Anderson localization for multi-particle systems ⋮ Weak chaos in the disordered nonlinear Schrödinger chain: destruction of Anderson localization by Arnold diffusion ⋮ Eigenvalue counting inequalities, with applications to Schrödinger operators ⋮ Scaling of chaos in strongly nonlinear lattices

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